Riemannian Optimization for LoRA on the Stiefel Manifold
This work improves parameter-efficient fine-tuning for large language models, offering a solution to a known bottleneck in LoRA optimization.
The paper tackles the problem of optimizer inefficiencies in LoRA fine-tuning for large language models, specifically addressing basis redundancy in the B matrix, and demonstrates that optimizing on the Stiefel manifold with orthogonality constraints consistently outperforms AdamW across benchmarks.
While powerful, large language models (LLMs) present significant fine-tuning challenges due to their size. Parameter-efficient fine-tuning (PEFT) methods like LoRA provide solutions, yet suffer from critical optimizer inefficiencies; notably basis redundancy in LoRA's $B$ matrix when using AdamW, which fundamentally limits performance. We address this by optimizing the $B$ matrix on the Stiefel manifold, imposing explicit orthogonality constraints that achieve near-perfect orthogonality and full effective rank. This geometric approach dramatically enhances parameter efficiency and representational capacity. Our Stiefel optimizer consistently outperforms AdamW across benchmarks with both LoRA and DoRA, demonstrating that geometric constraints are the key to unlocking LoRA's full potential for effective LLM fine-tuning.